Question

By selling oranges at RS.84 per dozen, a fruit vendor earns a profit of 12%. At what price must he sell each orange so as to earn a profit of
20%?​

Answer 1

Answer:-

Given:

SP of 12 oranges = ₹ 84.

Profit% = 12%

We know that,

CP = (100/100 + Profit%) * SP

⟹ CP of 12 oranges = (100/100 + 12) * 84

⟹ CP of 12 oranges = 100 * 84/112

⟹ CP of 12 oranges = ₹ 75

Now,

we have to find the SP of each orange to make a profit of 20% in the whole transaction.

So, Profit% = 20%.

⟹ CP = (100/100 + profit%) * SP

⟹ 75 = (100/100 + 20) * SP

⟹ 75 * 120/100 = SP

⟹ ₹ 90 = SP

Rs. 90 is the SP of 12 oranges.

So, SP of each orange = 90/12 = ₹ 7.5

∴ The vendor must sell each orange for ₹ 7.5 to make a profit of 20% in the whole transaction.

Answer 2

$\implies \sf{SP \: of \: 12 oranges = 84.} \\ \\ </p><p></p><p> \implies \sf{Profit\% = 12\%} \\ \\ </p><p></p><p> \implies\sf{We \: know \: that,} \\ \\ </p><p></p><p> \implies \sf{CP = ( \frac{100}{100} + Profit\%) \times SP} \\ \\ </p><p></p><p> \implies \sf{=CP \: of \: m \: 12 \: oranges =} \\ \\ \implies\sf{ ( \frac{100}{100} +12) \times 84} \\ \\ </p><p></p><p> \implies \sf{CP \: of \: 12 \: oranges \: 100 \times \frac{84}{112} } \\ \\ </p><p></p><p> \implies \sf{CP \: of \: 12 oranges \: = 75}</p><p>$

$\implies \sf{we \: have \: to \: find \: the \: SP \: of \: each \: } \\ \sf{orange \: to \: make \: a \: profit \: of \: } \\ \\ </p><p></p><p> \implies\sf{20\% in \: the \: whole \: transaction \: } \\ \\ </p><p></p><p> \implies\sf{So, Profit\% = 20\%} \\ \\ </p><p></p><p> \implies \sf{CP = ( \frac{100}{100} + profit\%) \times SP} \\ \\ </p><p></p><p> \implies \sf{75 = ( \frac{100}{100} + 20) \times SP} \\ \\ </p><p></p><p> \implies \sf{75 \times 120/100 = SP} \\ \\ </p><p></p><p> \implies\sf{ 90 = SP} \\ \\ </p><p></p><p> \implies \sf{Rs. \: 90 \: is \: the \: SP \: of \: 12 \: oranges \: .} \\ \\ </p><p></p><p> \implies \sf{So, \: SP \: of \: each \: orange \: \frac{90}{127.5} }$

$\huge\sf\underline{hence \: proved}$